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How do I solve log x + log (x-15)=2 ?
I don't understand how to set up this problem: How do I solve log x + log (x-15)=2
2 Answers
- ?Lv 76 years agoFavorite Answer
Note that one property of logarithms is that
log(a) + log(b) = log(ab)
for all logarithmic bases.
Now assuming that by log you are referring to base 10, since without the subscript, it is implied.
But
log(x) + log(x - 15) = 2
log(x(x - 15)) = 2
x(x - 15) = 10²
x² - 15x - 100 = 0
x = (15 ± √((-15)² - 4*1*(-100)))/(2*1)
= (15 ± √(225 + 400))/2
= (15 ± √(625))/2
= (15 ± 25)/2
Since log(a) is undefined for a ≤ 0.we must have that
x = (15 + 25)/2
ie
x = 20
